Yes, Christ did call his 12 Apostles. They did hold the authority of His Priesthood. However, where does scripture tell us that they passed it to anyone. Each of them were killed or banished, with no record of them ordaining another Pope to take Peter's place.
Again, I won't belabor this beyond this comment however it will be lengthy in order to properly and thoroughly answer your question.
Yes, the Holy Bible indeed records Christ passed on His power and authority to the Apostles and from them to other good men through Apostolic Succession.
The Holy Bible teaches the twelve Apostles were sent by Christ to lay the first foundation of His Church, the Catholic Church. With Christ as the Head cornerstone, Peter was chosen as the foundation rock and the Apostles the foundation stones.
Just before Jesus ascended into heaven, He gave them His power and authority and just as He had been sent He also sent them to continue His mission saying, “All authority in Heaven and earth has been given to Me. Go, therefore, and make disciples of all nations, baptizing them in the name of the Father and of the Son and of the Holy Ghost, teaching them to observe all that I have commanded you; and behold, I am with you all days, even unto the consummation of the world." St. Matt. 28:19-20.
So with the sacred power and authority Christ claimed in heaven and on earth, He sent them on their pastoral mission to all the world until the consummation of the world at the end of time. The doctrine of Apostolic succession means that the mission and power and authority to teach, rule and sanctify that Christ conferred on His Apostles perpetuated in the Church's episcopate. When Christ gave them the commission, He promised He would be with them “all days, to the end of the world.” verse 20. The promise of abiding divine assistance given in the context of the apostolic mandate implies that the mandate itself was to endure until the end of time.
But how was that to be done since the Apostles died?
Since Christ promised that His Church would endure until the end of time and that He would be with it always, the Church had to have apostolic continuity, teaching always what the Apostle's taught The Apostles, in order that the mission confided to them by Christ would continue after their deaths, appointed other men to continue the work they had begun.
Scripture teaches the how and when and who the Apostles appointed as their lawful successors to carry on their work.
Saul, renamed St.Paul, had been selected by Christ Himself; yet he was later ordained by Apostolic authority.
Acts 13:2-3, “As they were ministering to the Lord, and fasting, the Holy Ghost said to them, Separate me Saul and Barnabas for the work whereunto I have taken them. Then they, fasting and praying and imposing hands upon them, sent them away.”
If you read the Epistle of St.Paul to Titus you’ll see it records that St.Paul having preached the faith in the isle of Crete, he ordained Titus, bishop, and left him there to finish the work he had begun. St. Paul directs Titus to ordain bishops and priests for the different cities,showing him the principal qualities necessary for a bishop, also gives him particular advice for his own flock, exhorting him to hold the strictness of discipline, but seasoned with lenity. It was written about 33 years after Our Lord’s Ascension.
Here’s one verse of Titus 1:5. “For this cause I left thee in Crete that thou should set in order the things that are wanting, and should ordain priests in every city, as I had appointed thee.”
The Apostles acted collectively as officers of the Church which would become known as the Catholic Church. It got its name from a bishop passing through Smyrna on his way to Rome to die for “the faith of Jesus Christ.” Rom. 3:26. They exercised the 3 fold power of teaching, governing and sanctifying. Acts 1:12-26; 2:37-43; 4:35-37; 5:1-11; 28-41; 8:14-20. In Acts 5, there were 72 disciples appointed to carry on the work of the Apostles.
The Bible teaches that the office of the bishop, priests, etc. in the true Church comes by Divine appointment; i.e. God gives individuals a special vocation to this calling.
Hebrews 5:4, “And no man taketh this honor unto himself, but he that is called of God, as was Aaron.”
Hebrews 5:1, “For every high priest taken from among men is ordained for men in things pertaining to God, that he may offer both gifts and sacrifices for sins.” As far as offering sacrifice here, Christ ordered His Church to perpetuate that sacrificial rite for the continued sanctification of His followers , saying, “take ye and eat, this is My Body, take ye, this is My Blood, …Do this for a commemoration of Me.” St.Paul who wrote this text in Hebrews also bears witness that the sacrifical rite which Christ instituted at the Last Supper is to be perpetuated and that is exactly what he was doing. We know this from reading 1Corinthians 11:23-27. It gives the earliest and most detailed account of the Holy Eucharist and was written in Ephesus in 52-55 AD. The consecration formula quotes verbatim from a formula already in use in Apostolic times. So in short the Catholic Eucharistic liturgy celebrated at every Holy Mass is indeed the same one as the Apostles and implicitly their successors where commanded to celebrate in His memory.
St. Peter tells us in his letter that upon the death of these successors other proven men should be appointed to succeed them 1St. Peter 2: 4-5, 9, 12, 21, 25. Under the Apostles, a hierarchy began to appear with bishops, presbyter (priests) and deacons. Acts 6 relates to the appointment by the Apostles of the "seven". This is the second identifiable group of disciples entrusted to the ministry of the early Catholic Church. V.6 The Apostles establish the seven in their office or ministry through prayer and the “laying on of hands”, a rite that the early Church had adopted as of the conferring of a spiritual grace of office. The authority to carry out the ministry which implies a calling from God, is something he must receive through ordination, which the Apostles confer. (Today, it’s called the Sacrament of Holy Orders). God, not men, gives them a spiritual power which equips them to govern and teach the Christian community, administer the Sacraments, including the Mass and consecration of the Eucharist and preach the Word.
In 2Tim.1:6, Timothy received the grace of his ministry “through the laying on of hands" from St.Paul. 1TIm. 4:14 tells us that others were with St. Paul when he conferred the fullness of the priesthood on Timothy. Both Timothy and Titus were sent out and they ordained priests and deacons. 1Tim. 3:1; 5:17-22; Tit. 1:5.
St. Ignatius' writing in 107 AD supposes that the episcopate has been instituted for some time. He asserts that there is one bishop in every church to whom the presbyters (priests) and deacons must be subject. I can supply other Church Father’s writings which confirm the same and trace the line of bishops, priests and deacons down to the first century to the Apostles. Thus, a continuous hierarchy was established to continue the work of the Twelve. These men were given the Greek name, Episkopas, literally overseer, and in English, we term "bishop".
After St. Peter is St. Linus, then St.Cletus, and then St.Clement of Rome. I won’t here, but can name all 265 Popes and give the dates of their pontificate. Pope Clement rebukes them for a schism that had broken out among them. It's historical significance is shows the Bishop of Rome (the Pope), intervening authoritatively in the affairs of the Church to settle a dispute and indicates the primacy that was given to a successor of St. Peter. The epistle of Clement to the Corinthians witnesses to the belief of the Church in the last decade on the 1st century, with their ministry. He speaks of these bishops as having been constituted either by the Apostles themselves or that the Apostles had made provision for a succession in their ministry. Clement says that the Apostles installed bishops, and then laid down the rule that when these men passed on, others should be ordained and continue subsequently by “other eminent men”.
There is no doubt that from the writings of the Church Fathers, such as Ignatius of Antioch and Irenaeus, and with evidence from Scripture, that within 3 decades of the death of Christ, the Church had already hierarchically organized just as I have described. Thus the apostolic succession is maintained through the popes, who are successors to Peter as the Vicar of Christ, the bishops, successors to the Apostles, the priests, successors to those early priests, and the deacons.